Math203

Course Description form

Faculties and departments requiring this course (if any): Faculties of Engineering and of Science.

Objectives:  Prefer In points

On completion of the course, the students should be able to

• know about the basics of parameterization of plane curves, polar coordinates, and  conic section;
• use vectors in two and three dimensions to describe lines and planes in space;
• understand sketching of quadric surfaces;
• comprehend vector-valued functions and their use to describe the motion of objects through space;
• grasp the idea of the epsilon-delta definition  of the limit, and understand the methods for proving existence and non-existence of limit of functions of two/three variables;
• learn the idea of partial derivative and application of the chain rule;

          solve optimization problems without and with constraints. 

Contents: Prefer In points

1. Conic Sections and Polar Coordinates, Quadratic Equations and Rotations, Areas and Lengths in Polar Coordinates.
2. Vectors and the Geometry of Space, Lines and Planes in Space, Cylinders and Quadric Surfaces.
3. Vector-Valued Functions, Modeling Projectile Motion, Planetary Motion and Satellites.
4. Limits and Continuity in Higher Dimensions, Partial Derivatives, Directional Derivatives and Gradient Vectors, Optimization, Lagrange Multipliers, Taylor’s Formula for Two Variables.

Details 

 Unit I. Conic Sections and Polar Coordinates: Conic Sections and Quadratic   Equations, Classifying Conic Sections by Eccentricity, Quadratic Equations and Rotations, Conics and Parametric Equations; The Cycloid, Polar Coordinates, Graphing in Polar Coordinates, Areas and Lengths in Polar Coordinates, Conic Sections in Polar Coordinates.

Unit II. Vectors and the Geometry of Space: Three-Dimensional Coordinate Systems, Vectors, the Dot Product, the Cross Product, Lines and Planes in Space, Cylinders and Quadric Surfaces.

Unit III. Vector-Valued Functions and Motion in Space: Vector Functions, Modeling Projectile Motion, Arc Length and the Unit Tangent Vector T, Curvature and the Unit Normal Vector N, Torsion and the Unit Binomial Vector B, Planetary Motion and Satellites.

Unit IV. Partial Derivatives: Functions of Several Variables, Limits and Continuity in Higher Dimensions, Partial Derivatives, The Chain Rule, Directional Derivatives and Gradient Vectors, Tangent Planes and Differentials, Extreme Values and Saddle Points, Lagrange Multipliers, Partial Derivatives with Constrained Variables, Taylor’s Formula for Two Variables.

Course Outcomes:

A.   Knowledge:

     (Specific facts and knowledge of concepts, theories, formula etc.)

 The student will learn the basics of parameterization of plane curves,    conic    section, three dimensional geometry, vector-valued functions with applications, and calculus of several variables with applications.

     B-Cognitive Skills

     (Thinking, problem solving) 

The student will improve his/her logical thinking and imagination to conceive and         solve the practical problems using the knowledge learnt in this course. 

     C- Interpersonal skills and responsibilities

     (Group participation, leadership, personal responsibility, ethic and moral behavior,  capacity for  self directed learning)

The student is expected to carry out an independent investigation of the topic by    studying the available material, interacting with fellow students and the instructor to obtain sufficient information, and then analyse and manipulate this information to arrive at logical conclusions.   

     D- Analysis and communication:

     (communication, mathematical and IT skills)

Activities such as group discussion and report-writing play a key role in enhancing  communication skills. Working independently and jointly is another important factor for developing such skills.  Regular feedback on the completed oral/written assignments with constructive and moral boosting comments must be conveyed to the students in order to enhance such skills

Assessment methods for the above elements

Discussions, Homework, Periodic tests and final test

Text book: Only one

     Thomas' Calculus, 11^th Edition Media Upgrade, Addison Wesley, Pearson, 2008